Solve Combination Problem: Choose 4 Shoes from 5 Pairs

  • Thread starter ron_jay
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    Combination
In summary, when choosing 4 shoes from 5 pairs, there are 120 different combinations. Each shoe is considered as an individual item and cannot be counted as one choice. The formula for calculating combinations is nCr = n! / (r! x (n-r)!), and the order of the chosen shoes is not important. Additionally, each shoe can only be chosen once in a combination.
  • #1
ron_jay
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Homework Statement



A closet has 5 pairs of shoes. The number of ways in which 4
shoes can be chosen from it so that there will be no complete pair are?

Homework Equations



Permutation and Combination formulae

The Attempt at a Solution



I tried but couldn't figure it out anyway.
 
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  • #2
It would be a lot easier for us to tell you what you did wrong, if you showed us what you did.
 
  • #3
Since you don't want to have a pair you are only left with 5 shoes to pick from. Now choose 4 from that.
 

1. How many different combinations can be made when choosing 4 shoes from 5 pairs?

There are 5 possible choices for the first shoe, 4 for the second, 3 for the third, and 2 for the fourth, resulting in a total of 5 x 4 x 3 x 2 = 120 different combinations.

2. Can a pair of shoes be counted as one choice in this combination problem?

No, in this problem, each shoe is considered as an individual item, so a pair of shoes cannot be counted as one choice.

3. What is the formula for calculating combinations in this problem?

The formula for calculating combinations is nCr = n! / (r! x (n-r)!), where n represents the total number of items and r represents the number of items being chosen.

4. Is the order of the chosen shoes important in this combination problem?

No, the order of the chosen shoes is not important in this problem. As long as the same 4 shoes are chosen, it does not matter in which order they are selected.

5. Can a shoe be chosen more than once in a combination?

No, in this problem, each shoe can only be chosen once. The combination is made up of unique items and does not allow for repetition.

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